According to Nawalparasi police, six men who arrived by motorcycle torched the trucks after dousing them in petrol.
The flames engulfing the truck (numbered UP 32 BL 9696 and 38 V 3377) were extinguished by a fire brigade from district headquarters.
The Revolutionary Left Wing, the party which separated from the Maoists, began the protests on Thursday in the Lumbini area announcing it would not allow vehicles with Indian number plates to operate for a week.
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